Abstract
We consider weak solutions to the three dimensional Vlasov--Poisson system of equations, in either the attractive or the repulsive case, which are generated by data with finite space moments of order 2. We obtain a propagation result for any space moment of order $>2$. Under some suitable assumptions, a uniform bound on the macroscopic density is derived, leading to a uniqueness statement. Both results follow from the Hölder regularity satisfied by the corresponding DiPerna--Lions flow.
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